Question

How do you use implicit differentiation to find `(dy)/(dx)` given `x^3+y^3=1`?

Answer 1

`(dy)/(dx) =-x^2/y^2`

Explanation:

Differentiate the equation with respect to `x`:

`d/(dx) (x^3+y^3) = d/(dx) 1`

`3x^2 +3y^2(dy)/(dx) = 0`

`(dy)/(dx) =-x^2/y^2`